The firm is looking to use a $3.3 billion permanent vehicle, raised in 2014, to buy ownership stakes in hedge-fund and private-equity managers

The world’s largest private-equity firm by assets under management is looking to buy ownership stakes in its smaller peers.

Blackstone Group LP is looking to use a $3.3 billion permanent vehicle—a pool with an indefinite fund life—raised in 2014 to buy ownership stakes in hedge-fund managers and to take minority stakes in established private-equity firms, said people familiar with the situation.